A vertical spring supports a 5 kg mass at equilibrium by stretching 3 cm. How far would the same spring have to stretch to support a 7 kg mass at equilibrium?

A simple design for a bathroom scale is to place a platform to stand on atop a spring. If you want the scale to be able to measure weights up to 1500 N, and the scale needs to be 3 cm tall, what is the minimum spring constant required for the scale to work?

A mass-spring system has a period on Earth of 1.7 s. On the moon, where gravity is about one-sixth that of the Earth, what is the period of the spring?

A small block of mass m is on a frictionless table and is attached to a horizontal spring. The spring has stiffness ks and a relaxed length L. The other end of the spring is fastened to a fixed point at the center of the table. The block slides on the table in a circular path of radius R > L. How long does it take for the block to go around once?
1. T = √ 3π2mL2 / ksR2
2. T = √ 4πmR / ksL
3. T = √ 4π2mR2 / ksL
4. T = √ 4πmR / ks (R − L)
5. T = √ 4π2mR2 / ks(R − L)2
6. T = √ 2πmR / ks(R − L)
7. T = √ 3π2mR2 / ks(R − L)
8. T = √ 4π2mR / ks(R − L)
9. T = √ 4πmR / ks(L − R)
10. T = √ 4π2mR / ks(L − R)

A 3 kg mass slides without friction along the ground at 12 m/s. If the mass contacts a spring, with a force constant of 100 N/m, compresses the spring to a maximum extent, and is then propeled in the opposite direction, how long is the mass in contact with the spring for?